Background: I have studied mathematics at university (mainly algebraic and arithmetic geometry), but for many reasons I am now a PhD student in computer science. However, at the end of the first year all PhD students have to pass an interview, and if they don't they can't continue with the process. During the preparation to this interview, I have understood that I was missing to explain why my research was relevant within the field; more specifically, which impact it can have, which applications can be developed from this. And I was wondering: is this a matter of being somehow different from my collegues? I mean, I am enthusiastic about the project I'm working on because it's an interesting project, and not because I'm sure it'll have many applications (well, now I'm a bit more convinced about its applications too). So the question is: what am I?

More in general, what is a mathematician? Of course, for most of you it's clear that you are. But what about those who work in some "in-between" field?

I guess that also being recognized as mathematicians by a community is a big part of beeing / feeling a mathematician. But for example, the questions generally posted on Mathoverflow are often out-of-my-reach. However, I feel that the methods I use for solving problems in the area I'm studying now use mathematical methods, in a non-trivial way (I mean, I don't just solve an integral to find a number, I'm building a formal theory behind this approach to the problem).

More in general, I imagine that there should be plenty of people, with a mathematical background, who work in applications, like economics for example, who do something similar to what I do: are they mathematicians?

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What do you intend to do with an answer to this question?
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Qiaochu YuanFeb 2 '11 at 16:36

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klaraspina, I'm sympathetic to your predicament, but at the same time I think this probably isn't the right place to be asking your question. It seems unlikely that there's any good answer to "what is a mathematician?", and really what you're after is some advice. Maybe someone can suggest a better place to ask for it.
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Tom LeinsterFeb 2 '11 at 16:37

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Wouldn't any answer that excludes X from being a mathematician be extremely hurtful to X?
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Zev ChonolesFeb 2 '11 at 16:38

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@Zev, Igor--not necessarily; it depends on the vestment X has in being a mathematician.
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drbobmeisterFeb 2 '11 at 16:52

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As a self proclaimed "lover of math" (see my MO profile page), I would encourage anyone who wishes to pursue mathematics on any level to do so!
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drbobmeisterFeb 2 '11 at 17:30